The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  X  X 4X 2X 3X  0  X 3X 3X 3X 5X 2X 2X  X 4X 2X 3X 4X  0  0 4X  X 5X  X 3X 4X 4X 3X 6X 4X 3X 4X 4X  0 6X  X 5X 5X 5X 6X 3X 5X 6X 3X 4X  X 2X  X 6X 5X 5X 2X 6X  0 2X  0  0  X 5X  0 2X
 0  0  X  0 5X 4X 3X 5X 6X 3X 3X 3X 5X 5X 4X  0  0 3X  X 4X 2X  X  X 5X  0  X 2X  X  X 3X 2X 6X 5X 5X  X 2X 6X 6X 6X 4X 3X 3X 5X  X 3X 4X  X 2X 5X 6X 6X 5X 4X  0  0  X 2X 3X 4X 6X 5X 2X 2X 6X 5X
 0  0  0  X 5X  X 2X 6X 6X 4X  X  0 2X 6X 6X 5X  X 2X 5X  X  X 3X 2X 4X 5X 5X 2X 2X  0 4X 4X  X 5X 2X 3X 3X 5X 6X 4X 2X 6X 3X 3X 6X 3X 2X  X 3X 3X 4X 3X 6X 5X 2X 5X 3X 2X 6X 5X 3X 5X 5X  X 2X 4X

generates a code of length 65 over Z7[X]/(X^2) who´s minimum homogenous weight is 371.

Homogenous weight enumerator: w(x)=1x^0+420x^371+822x^378+3948x^385+10956x^392+192x^399+144x^406+84x^413+60x^420+54x^427+54x^434+42x^441+24x^448+6x^455

The gray image is a linear code over GF(7) with n=455, k=5 and d=371.
This code was found by Heurico 1.16 in 81.9 seconds.